I don’t feel links to Twitter discussions have a place on this site.
If it’s an official announcement, there’s almost always a link to a site - this should be submitted instead.
If it’s a “story” that unfolds on Twitter, make the bare effort to “unroll it” using one of the many services available for this, or by authoring a post yourself with a summary, along with links to the relevant tweets.
Edit - two recent examples
This tweet has a screenshot, but no source attributing it to Disqus. The only link is to the author’s own blog.
This is a perfectly reasonable tweet in that it’s the author asking his Twitter circle for help, but it’s a terrible fit for Lobste.rs, where the community might be interested in content like a hypothetical blog post titled “
less sucks for files larger than X GB. Here are a couple of alternatives”.